Precompact noncompact reflexive abelian groups

TL;DR

This paper constructs various examples of precompact, noncompact, reflexive abelian groups, exploring their properties and relationships, including pseudocompactness and quotient structures, advancing the understanding of topological group reflexivity.

Contribution

It provides new examples of reflexive abelian groups with diverse compactness properties and establishes quotient relationships involving pseudocompact groups.

Findings

Existence of precompact, non-pseudocompact reflexive groups

Examples of pseudocompact and countably compact reflexive groups

Every pseudocompact abelian group is a quotient of a reflexive pseudocompact group

Abstract

We present a series of examples of precompact, noncompact, reflexive topological Abelian groups. Some of them are pseudocompact or even countably compact, but we show that there exist precompact non-pseudocompact reflexive groups as well. It is also proved that every pseudocompact Abelian group is a quotient of a reflexive pseudocompact group with respect to a closed reflexive pseudocompact subgroup.